Answer:
By creating this system of equations, you can solve for the intersection point of the two lines, which is where they meet on the graph. This process allows you to analyze the relationship between the lines and their properties based on the slopes and y-intercepts determined from the graph.
Step-by-step explanation:
To write a system of linear equations representing lines from a graph with two plotted lines, you need to gather information from the graph to determine the slopes and y-intercepts of each line. Once you have this information, you can write the equations in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.
Here's a general outline to help you write the system of linear equations:
1. Identify the slopes (m1, m2) and y-intercepts (b1, b2) of the two lines from the graph.
2. Write the equations of the lines in slope-intercept form:
- Line 1: \( y = m1x + b1 \)
- Line 2: \( y = m2x + b2 \)
3. Ensure that each equation represents the corresponding line accurately based on the graph.
4. Combine the two equations into a system of linear equations:
\[
\begin{cases}
y = m1x + b1 \\
y = m2x + b2
\end{cases}
\]
